Heat the oven to 350°F. Pour the melted butter into a 9-inch round cake pan, then tilt the pan so the butter coats the bottom and runs slightly up the sides. Sprinkle the brown sugar evenly over the bottom of the pan.

Pat the pineapple slices very dry with paper towels. Place one slice in the center and arrange six more around it. If desired, halve three more slices to fill the edge. Place a cherry in the hole of each whole slice and tuck any extra cherries into the open spaces.

In a medium bowl, whisk together the flour, baking powder, and salt. In a large measuring cup, whisk the sour cream and milk together.

In a mixer bowl, beat the butter until creamy. Add granulated sugar and beat on medium until light and fluffy. Add the eggs one at a time, mixing well after each addition. Stir in vanilla.

On low speed, add one-third of the flour mixture, then half of the sour cream mixture. Repeat this pattern, finishing with the last of the flour. Stop mixing as soon as everything is combined.

Spread the batter evenly over the fruit. Set the pan on a baking sheet and bake for 40 to 45 minutes until a toothpick inserted comes out with a few moist crumbs. Cover loosely with foil if browning too quickly.

Let the cake cool in the pan on a wire rack for 15 minutes. Place a serving plate over the pan and flip it in one confident motion. Let cool for at least 20 more minutes before slicing.